In [1]}, Rudnick and Waxman study the distribution of angles \(\theta _\mathfrak {p}\) , where \(\mathfrak {p}=\langle \alpha \rangle \)  is an ideal of the Gaussian integers \(\mathbb {Z}[i]\) , and \(\theta _\mathfrak {p}=\arg \alpha \) , namely,
\(u(\alpha ):=\left(\frac{\alpha }{\overline{\alpha }}\right)^2 =e^{4i \theta _\mathfrak {p}}.\) 
